Answer: 866.25ft
Explanation:
Pressure drop= 16.3 psi
1 feet of water column= 0.4335psi
x= 16.3psi
Therefore, head loss of water= 16.3/0.4335=37.6ft
In inches, head loss of water= 37.6 × 12=451.2 inches
Q= 1.64ft^2/s
A= pi/4 D^2
Where D= 6 inches, 0.5ft
A= 3.142/4 × (0.5)^2
A= 0.1962ft^2
V= Q/A= 1.64/ 0.1962
V= 8.35ft/s, 100.28 in/s
REGNOLD'S NO
Re= SvD/ μ=
Where, D= 6 inches, V= 100.28 inches/s, S=62.4lb/ft^3= 0.03611lb/inches^3
At 68F, Dynamic viscosity μ= 1.0016× 10^-3NS/m^2
1psi= 6895N/m^3
μ= 1.0016× 10^-3NS/m^2/6895N/m^3
μ= 1.452× 10^-7lbs/ins^2
Re= 0.03611× 100. 28×6/1.42×10^-7
Re= 1.49×10^8
e/D----- Relative roughness
e= 0.0005ft
e/D= 0.001
Therefore, for Re= 1.49×10^8 and e/D= 0.001
F=0.02
Head loss is given by Dancy-Weisbach formula
hL= fLV^2/2gD
Wherr g= 9.81m/s^2= 386.12inches/s^2
451.2= 0.02×L×(100.28^2)/2 × 386.12inches/s^2× 6
L= 10395inches
L= 10395/12= 866.25ft
Therefore, the length of pipe is 866.25ft.
